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Critical gravitational collapse of a perfect fluid: nonspherical perturbations

Critical gravitational collapse of a perfect fluid: nonspherical perturbations
Critical gravitational collapse of a perfect fluid: nonspherical perturbations
Continuously self-similar (CSS) solutions for the gravitational collapse of a spherically symmetric perfect fluid, with the equation of state p=??, with 0<?<1 a constant, are constructed numerically and their linear perturbations, both spherical and nonspherical, are investigated. The l=1 axial perturbations admit an analytical treatment. All others are studied numerically. For intermediate equations of state, with 1/9<??0.49, the CSS solution has one spherical growing mode, but no nonspherical growing modes. That suggests that it is a critical solution even in (slightly) nonspherical collapse. For this range of ? we predict the critical exponent for the black hole angular momentum to be 5(1+3?)/3(1+?) times the critical exponent for the black hole mass. For ?=1/3 this gives an angular momentum critical exponent of ??0.898, correcting a previous result. For stiff equations of state, 0.49??<1, the CSS solution has one spherical and several nonspherical growing modes. For soft equations of state, 0<?<1/9, the CSS solution has 1+3 growing modes: a spherical one, and an l=1 axial mode (with m=-1,0,1)
1550-7998
084021-[22pp]
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc

Gundlach, Carsten (2002) Critical gravitational collapse of a perfect fluid: nonspherical perturbations. Physical Review D, 65 (8), 084021-[22pp]. (doi:10.1103/PhysRevD.65.084021).

Record type: Article

Abstract

Continuously self-similar (CSS) solutions for the gravitational collapse of a spherically symmetric perfect fluid, with the equation of state p=??, with 0<?<1 a constant, are constructed numerically and their linear perturbations, both spherical and nonspherical, are investigated. The l=1 axial perturbations admit an analytical treatment. All others are studied numerically. For intermediate equations of state, with 1/9<??0.49, the CSS solution has one spherical growing mode, but no nonspherical growing modes. That suggests that it is a critical solution even in (slightly) nonspherical collapse. For this range of ? we predict the critical exponent for the black hole angular momentum to be 5(1+3?)/3(1+?) times the critical exponent for the black hole mass. For ?=1/3 this gives an angular momentum critical exponent of ??0.898, correcting a previous result. For stiff equations of state, 0.49??<1, the CSS solution has one spherical and several nonspherical growing modes. For soft equations of state, 0<?<1/9, the CSS solution has 1+3 growing modes: a spherical one, and an l=1 axial mode (with m=-1,0,1)

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Published date: April 2002

Identifiers

Local EPrints ID: 29188
URI: https://eprints.soton.ac.uk/id/eprint/29188
ISSN: 1550-7998
PURE UUID: 089e169e-cc7f-4c36-a764-dac7e2007e5f
ORCID for Carsten Gundlach: ORCID iD orcid.org/0000-0001-9585-5375

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Date deposited: 12 May 2006
Last modified: 20 Jul 2018 00:34

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